310 THE PRINCIPLES OF SCIENCE. 



with the degree of esteem proportionate to its proba- 

 bility. We go through the same steps as before. 



(1) We frame an hypothesis. 



(2) We deduce the probability of various series of pos- 

 sible consequences. 



(3) We compare the consequences with the particular 

 facts, and observe the probability that such facts would 

 happen under the hypothesis. 



The above processes must be performed for every con- 

 ceivable hypothesis, and then the absolute probability of 

 each will be yielded by the principle of the inverse 

 method (p. 279). As in the case of certainty we accept 

 that hypothesis which certainly gives the required results, 

 so now we accept as most probable that hypothesis which 

 most probably gives the results ; but we are obliged to 

 entertain at the same time all other hypotheses with 

 degrees of probability proportionate to the probabilities 

 that they would give the results. 



So far we have treated only of the process by which 

 we pass from special facts to general laws, that inverse 

 application of deduction which constitutes induction. 

 But the direct employment of deduction is often com- 

 bined with the inverse. No sooner have we established 

 a general law, than the mind rapidly draws other particular 

 consequences from it. In geometry we may almost seem 

 to infer that because one equilateral triangle is equi- 

 angular, therefore another is so. In reality it is not 

 because one is that another is, but because all are. The 

 geometrical conditions are perfectly general, and by what is 

 sometimes called parity of reasoning whatever is true of 

 one equilateral triangle, so far as it is equilateral, is true 

 of all equilateral triangles. 



Similarly, in all other cases of inductive inference, 

 where we seem to pass from some particular instances to 

 a new instance, we go through the same process. We 



